The Eagles head to Ashton Gate for the first time since August 2013 when they were knocked out of the same competition by City, and the recently redeveloped stadium hasn't been a happy hunting ground for Palace who haven't won at the venue since 1980.
Two years later, Hodgson would spend a short time as Robins manager in what was his first managerial job in England, but he lasted just four months in charge, having previously been assistant to Bob Houghton.
Robins looking for a third scalp
Saturday saw the Robins lose for the first time in 13 games as Leeds United ran out convincing 3-0 winners at Ashton Gate, seeing them slip out of the Championship play-off places in the process.
However, having finished 17th last season, Lee Johnson's side will be buoyed by their start to the campaign, especially their run to this stage of the competition. After beating Plymouth Argyle in the first round, they have also knocked out Premier League duo Watford and Stoke City, with the Potters dispatched 2-0 at Ashton Gate last month.
Bobby Reid tops their goalscoring charts with eight goals in all competitions so far, with £5 million summer arrival Famara Diedhiou adding another six.
View from the opposition
Lee Johnson: "I believe in the squad. It's more for me about ticking the boxes: have we got the height, can we match the markers, have we got speed, have we got someone who can unlock a door, have we got energy in the middle?
"It's more about putting together a team who will be effective on that particular day."
Team news
Former Aston Villa defender Nathan Baker will miss the game with a knee injury, while doubts remain over Korey Smith who has a tight hamstring as well as Jamie Patterson who has been suffering with illness.
Meanwhile, loanees Cauley Woodrow and Jonathan Leko are cup-tied having played earlier in the competition and Matty Taylor may face a ban after receiving a straight red card in the defeat to Leeds, although the club will appeal.
Eros Pisano is close to returning following a knee complaint and Milan Djuric successfully played 45 minutes for the Robins' under-23s on Friday.
Hodgson has indicated he will make changes to his team, suggesting in his post-match press conference on Tyneside that James Tomkins, Martin Kelly and Wayne Hennessey could all be involved as he looks to evaluate more of his squad.
Matchday officials
Tim Robinson takes charge of Palace for the first time in his career on Tuesday night, and the Football League official has been busy in his 16 appointments to date, dishing out seven red cards already this term, including one to Watford's Jose Holebas in their second round defeat against City.
Referee: Tim Robinson
Assistant Refs: Andrew Fox and Mark Jones
Fourth Official: Andy Davies
Ticket and Travel Information
Tickets are still on sale to season ticket holders and paid members at two person.
Adults - £12
Over 65s - £8
Under-22s - £8
Under-19s - £5
Coaches will depart Selhurst Park at 2pm, priced at £19 per seat.
Tickets and coaches can be booked online, by calling the ticket line on 08712 000 071, or in person at the Box Office.
The Robins have confirmed that over 18,000 tickets have already been snapped up for the cup tie.
Extra Time and Penalties
If the match is drawn after 90 minutes the tie will go to extra-time and then penalties.
League Cup fixtures do not go to replays right up until the semi-final stage.
This season, there is also the addition of ABBA penalties for drawn ties if it goes past extra-time.
Each team then alternates in taking two penalties until a result is achieved.
The idea behind the change is to take away the unfair disadvantage the team that takes the second penalty supposedly has when they have to kick to stay in the game.
Live coverage
If you can’t make it to Ashton Gate, there will be live commentary on Palace Player, updates on Twitter, with highlights available on Palace TV later in the week.